Simple physics power and work question (highschool level)

Question

Question 19:A 50.0 kg student runs up three flight of stairs at constant velocity, a vertical distance of 10.0 m. The first time it takes her 9.81 s. The second time it takes her 19.62 s. What was the power she exerted for both times up the stairs? (Hint: first find the work done) (answer: 1st time: 500W, 2nd time: 250W) I just need the know how was this answer found?

Answer 1

power = work/time

work = Force * distance (in same direction)

The force that your body needs to counteract to get up the stairs at a constant velocity is the weight of your body

Weight = mg = (50)(9.8) = 490N which points down so the force you apply F = 490N which points upward

Distance that you travel = 10.0m upward

Work = 490*10 = 4900 J

This work is the same in both scenarios because you are fighting the same force and traveling the same height. The power is different because the times are different.

power 1 = 4900/9.81 = 500 Watts

power 2 = 4900/19.62 = 250 Watts